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A posteriori error estimate for the Stokes–Darcy system
Author(s) -
Cui Ming,
Yan Ningning
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1422
Subject(s) - piecewise , a priori and a posteriori , mathematics , finite element method , quadratic equation , residual , darcy's law , stokes flow , element (criminal law) , mathematical optimization , porous medium , mathematical analysis , calculus (dental) , algorithm , geometry , porosity , flow (mathematics) , law , physics , medicine , philosophy , geotechnical engineering , dentistry , epistemology , political science , engineering , thermodynamics
We consider the a posteriori error estimates for finite element approximations of the Stokes–Darcy system. The finite element spaces adopted are the Hood–Taylor element for the velocity and the pressure in fluid region and conforming piecewise quadratic element for the pressure in porous media region. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient. Copyright © 2011 John Wiley & Sons, Ltd.